1 /* Chains of recurrences.
2 Copyright (C) 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010
3 Free Software Foundation, Inc.
4 Contributed by Sebastian Pop <pop@cri.ensmp.fr>
6 This file is part of GCC.
8 GCC is free software; you can redistribute it and/or modify it under
9 the terms of the GNU General Public License as published by the Free
10 Software Foundation; either version 3, or (at your option) any later
13 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
14 WARRANTY; without even the implied warranty of MERCHANTABILITY or
15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
18 You should have received a copy of the GNU General Public License
19 along with GCC; see the file COPYING3. If not see
20 <http://www.gnu.org/licenses/>. */
22 /* This file implements operations on chains of recurrences. Chains
23 of recurrences are used for modeling evolution functions of scalar
29 #include "coretypes.h"
33 #include "tree-pretty-print.h"
35 #include "tree-flow.h"
36 #include "tree-chrec.h"
37 #include "tree-pass.h"
40 #include "tree-scalar-evolution.h"
44 /* Extended folder for chrecs. */
46 /* Determines whether CST is not a constant evolution. */
49 is_not_constant_evolution (const_tree cst)
51 return (TREE_CODE (cst) == POLYNOMIAL_CHREC);
54 /* Fold CODE for a polynomial function and a constant. */
57 chrec_fold_poly_cst (enum tree_code code,
64 gcc_assert (TREE_CODE (poly) == POLYNOMIAL_CHREC);
65 gcc_assert (!is_not_constant_evolution (cst));
66 gcc_assert (type == chrec_type (poly));
71 return build_polynomial_chrec
72 (CHREC_VARIABLE (poly),
73 chrec_fold_plus (type, CHREC_LEFT (poly), cst),
77 return build_polynomial_chrec
78 (CHREC_VARIABLE (poly),
79 chrec_fold_minus (type, CHREC_LEFT (poly), cst),
83 return build_polynomial_chrec
84 (CHREC_VARIABLE (poly),
85 chrec_fold_multiply (type, CHREC_LEFT (poly), cst),
86 chrec_fold_multiply (type, CHREC_RIGHT (poly), cst));
89 return chrec_dont_know;
93 /* Fold the addition of two polynomial functions. */
96 chrec_fold_plus_poly_poly (enum tree_code code,
102 struct loop *loop0 = get_chrec_loop (poly0);
103 struct loop *loop1 = get_chrec_loop (poly1);
104 tree rtype = code == POINTER_PLUS_EXPR ? sizetype : type;
108 gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC);
109 gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC);
110 if (POINTER_TYPE_P (chrec_type (poly0)))
111 gcc_assert (chrec_type (poly1) == sizetype);
113 gcc_assert (chrec_type (poly0) == chrec_type (poly1));
114 gcc_assert (type == chrec_type (poly0));
117 {a, +, b}_1 + {c, +, d}_2 -> {{a, +, b}_1 + c, +, d}_2,
118 {a, +, b}_2 + {c, +, d}_1 -> {{c, +, d}_1 + a, +, b}_2,
119 {a, +, b}_x + {c, +, d}_x -> {a+c, +, b+d}_x. */
120 if (flow_loop_nested_p (loop0, loop1))
122 if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
123 return build_polynomial_chrec
124 (CHREC_VARIABLE (poly1),
125 chrec_fold_plus (type, poly0, CHREC_LEFT (poly1)),
126 CHREC_RIGHT (poly1));
128 return build_polynomial_chrec
129 (CHREC_VARIABLE (poly1),
130 chrec_fold_minus (type, poly0, CHREC_LEFT (poly1)),
131 chrec_fold_multiply (type, CHREC_RIGHT (poly1),
132 SCALAR_FLOAT_TYPE_P (type)
133 ? build_real (type, dconstm1)
134 : build_int_cst_type (type, -1)));
137 if (flow_loop_nested_p (loop1, loop0))
139 if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
140 return build_polynomial_chrec
141 (CHREC_VARIABLE (poly0),
142 chrec_fold_plus (type, CHREC_LEFT (poly0), poly1),
143 CHREC_RIGHT (poly0));
145 return build_polynomial_chrec
146 (CHREC_VARIABLE (poly0),
147 chrec_fold_minus (type, CHREC_LEFT (poly0), poly1),
148 CHREC_RIGHT (poly0));
151 /* This function should never be called for chrecs of loops that
152 do not belong to the same loop nest. */
153 gcc_assert (loop0 == loop1);
155 if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
157 left = chrec_fold_plus
158 (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
159 right = chrec_fold_plus
160 (rtype, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
164 left = chrec_fold_minus
165 (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
166 right = chrec_fold_minus
167 (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
170 if (chrec_zerop (right))
173 return build_polynomial_chrec
174 (CHREC_VARIABLE (poly0), left, right);
179 /* Fold the multiplication of two polynomial functions. */
182 chrec_fold_multiply_poly_poly (tree type,
188 struct loop *loop0 = get_chrec_loop (poly0);
189 struct loop *loop1 = get_chrec_loop (poly1);
193 gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC);
194 gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC);
195 gcc_assert (chrec_type (poly0) == chrec_type (poly1));
196 gcc_assert (type == chrec_type (poly0));
198 /* {a, +, b}_1 * {c, +, d}_2 -> {c*{a, +, b}_1, +, d}_2,
199 {a, +, b}_2 * {c, +, d}_1 -> {a*{c, +, d}_1, +, b}_2,
200 {a, +, b}_x * {c, +, d}_x -> {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x. */
201 if (flow_loop_nested_p (loop0, loop1))
202 /* poly0 is a constant wrt. poly1. */
203 return build_polynomial_chrec
204 (CHREC_VARIABLE (poly1),
205 chrec_fold_multiply (type, CHREC_LEFT (poly1), poly0),
206 CHREC_RIGHT (poly1));
208 if (flow_loop_nested_p (loop1, loop0))
209 /* poly1 is a constant wrt. poly0. */
210 return build_polynomial_chrec
211 (CHREC_VARIABLE (poly0),
212 chrec_fold_multiply (type, CHREC_LEFT (poly0), poly1),
213 CHREC_RIGHT (poly0));
215 gcc_assert (loop0 == loop1);
217 /* poly0 and poly1 are two polynomials in the same variable,
218 {a, +, b}_x * {c, +, d}_x -> {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x. */
221 t0 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
224 t1 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_RIGHT (poly1));
225 t1 = chrec_fold_plus (type, t1, chrec_fold_multiply (type,
227 CHREC_LEFT (poly1)));
229 t2 = chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
230 /* "a*d + b*c + b*d". */
231 t1 = chrec_fold_plus (type, t1, t2);
233 t2 = chrec_fold_multiply (type, SCALAR_FLOAT_TYPE_P (type)
234 ? build_real (type, dconst2)
235 : build_int_cst (type, 2), t2);
237 var = CHREC_VARIABLE (poly0);
238 return build_polynomial_chrec (var, t0,
239 build_polynomial_chrec (var, t1, t2));
242 /* When the operands are automatically_generated_chrec_p, the fold has
243 to respect the semantics of the operands. */
246 chrec_fold_automatically_generated_operands (tree op0,
249 if (op0 == chrec_dont_know
250 || op1 == chrec_dont_know)
251 return chrec_dont_know;
253 if (op0 == chrec_known
254 || op1 == chrec_known)
257 if (op0 == chrec_not_analyzed_yet
258 || op1 == chrec_not_analyzed_yet)
259 return chrec_not_analyzed_yet;
261 /* The default case produces a safe result. */
262 return chrec_dont_know;
265 /* Fold the addition of two chrecs. */
268 chrec_fold_plus_1 (enum tree_code code, tree type,
271 tree op1_type = code == POINTER_PLUS_EXPR ? sizetype : type;
273 if (automatically_generated_chrec_p (op0)
274 || automatically_generated_chrec_p (op1))
275 return chrec_fold_automatically_generated_operands (op0, op1);
277 switch (TREE_CODE (op0))
279 case POLYNOMIAL_CHREC:
280 switch (TREE_CODE (op1))
282 case POLYNOMIAL_CHREC:
283 return chrec_fold_plus_poly_poly (code, type, op0, op1);
286 if (tree_contains_chrecs (op1, NULL))
287 return chrec_dont_know;
290 if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
291 return build_polynomial_chrec
292 (CHREC_VARIABLE (op0),
293 chrec_fold_plus (type, CHREC_LEFT (op0), op1),
296 return build_polynomial_chrec
297 (CHREC_VARIABLE (op0),
298 chrec_fold_minus (type, CHREC_LEFT (op0), op1),
303 if (tree_contains_chrecs (op0, NULL))
304 return chrec_dont_know;
307 switch (TREE_CODE (op1))
309 case POLYNOMIAL_CHREC:
310 if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
311 return build_polynomial_chrec
312 (CHREC_VARIABLE (op1),
313 chrec_fold_plus (type, op0, CHREC_LEFT (op1)),
316 return build_polynomial_chrec
317 (CHREC_VARIABLE (op1),
318 chrec_fold_minus (type, op0, CHREC_LEFT (op1)),
319 chrec_fold_multiply (type, CHREC_RIGHT (op1),
320 SCALAR_FLOAT_TYPE_P (type)
321 ? build_real (type, dconstm1)
322 : build_int_cst_type (type, -1)));
325 if (tree_contains_chrecs (op1, NULL))
326 return chrec_dont_know;
331 if ((tree_contains_chrecs (op0, &size)
332 || tree_contains_chrecs (op1, &size))
333 && size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
334 return build2 (code, type, op0, op1);
335 else if (size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
336 return fold_build2 (code, type,
337 fold_convert (type, op0),
338 fold_convert (op1_type, op1));
340 return chrec_dont_know;
346 /* Fold the addition of two chrecs. */
349 chrec_fold_plus (tree type,
354 if (automatically_generated_chrec_p (op0)
355 || automatically_generated_chrec_p (op1))
356 return chrec_fold_automatically_generated_operands (op0, op1);
358 if (integer_zerop (op0))
359 return chrec_convert (type, op1, NULL);
360 if (integer_zerop (op1))
361 return chrec_convert (type, op0, NULL);
363 if (POINTER_TYPE_P (type))
364 code = POINTER_PLUS_EXPR;
368 return chrec_fold_plus_1 (code, type, op0, op1);
371 /* Fold the subtraction of two chrecs. */
374 chrec_fold_minus (tree type,
378 if (automatically_generated_chrec_p (op0)
379 || automatically_generated_chrec_p (op1))
380 return chrec_fold_automatically_generated_operands (op0, op1);
382 if (integer_zerop (op1))
385 return chrec_fold_plus_1 (MINUS_EXPR, type, op0, op1);
388 /* Fold the multiplication of two chrecs. */
391 chrec_fold_multiply (tree type,
395 if (automatically_generated_chrec_p (op0)
396 || automatically_generated_chrec_p (op1))
397 return chrec_fold_automatically_generated_operands (op0, op1);
399 switch (TREE_CODE (op0))
401 case POLYNOMIAL_CHREC:
402 switch (TREE_CODE (op1))
404 case POLYNOMIAL_CHREC:
405 return chrec_fold_multiply_poly_poly (type, op0, op1);
408 if (tree_contains_chrecs (op1, NULL))
409 return chrec_dont_know;
412 if (integer_onep (op1))
414 if (integer_zerop (op1))
415 return build_int_cst (type, 0);
417 return build_polynomial_chrec
418 (CHREC_VARIABLE (op0),
419 chrec_fold_multiply (type, CHREC_LEFT (op0), op1),
420 chrec_fold_multiply (type, CHREC_RIGHT (op0), op1));
424 if (tree_contains_chrecs (op0, NULL))
425 return chrec_dont_know;
428 if (integer_onep (op0))
431 if (integer_zerop (op0))
432 return build_int_cst (type, 0);
434 switch (TREE_CODE (op1))
436 case POLYNOMIAL_CHREC:
437 return build_polynomial_chrec
438 (CHREC_VARIABLE (op1),
439 chrec_fold_multiply (type, CHREC_LEFT (op1), op0),
440 chrec_fold_multiply (type, CHREC_RIGHT (op1), op0));
443 if (tree_contains_chrecs (op1, NULL))
444 return chrec_dont_know;
447 if (integer_onep (op1))
449 if (integer_zerop (op1))
450 return build_int_cst (type, 0);
451 return fold_build2 (MULT_EXPR, type, op0, op1);
460 /* Evaluate the binomial coefficient. Return NULL_TREE if the intermediate
461 calculation overflows, otherwise return C(n,k) with type TYPE. */
464 tree_fold_binomial (tree type, tree n, unsigned int k)
466 unsigned HOST_WIDE_INT lidx, lnum, ldenom, lres, ldum;
467 HOST_WIDE_INT hidx, hnum, hdenom, hres, hdum;
471 /* Handle the most frequent cases. */
473 return build_int_cst (type, 1);
475 return fold_convert (type, n);
477 /* Check that k <= n. */
478 if (TREE_INT_CST_HIGH (n) == 0
479 && TREE_INT_CST_LOW (n) < k)
483 lnum = TREE_INT_CST_LOW (n);
484 hnum = TREE_INT_CST_HIGH (n);
486 /* Denominator = 2. */
490 /* Index = Numerator-1. */
494 lidx = ~ (unsigned HOST_WIDE_INT) 0;
502 /* Numerator = Numerator*Index = n*(n-1). */
503 if (mul_double (lnum, hnum, lidx, hidx, &lnum, &hnum))
506 for (i = 3; i <= k; i++)
512 lidx = ~ (unsigned HOST_WIDE_INT) 0;
517 /* Numerator *= Index. */
518 if (mul_double (lnum, hnum, lidx, hidx, &lnum, &hnum))
521 /* Denominator *= i. */
522 mul_double (ldenom, hdenom, i, 0, &ldenom, &hdenom);
525 /* Result = Numerator / Denominator. */
526 div_and_round_double (EXACT_DIV_EXPR, 1, lnum, hnum, ldenom, hdenom,
527 &lres, &hres, &ldum, &hdum);
529 res = build_int_cst_wide (type, lres, hres);
530 return int_fits_type_p (res, type) ? res : NULL_TREE;
533 /* Helper function. Use the Newton's interpolating formula for
534 evaluating the value of the evolution function. */
537 chrec_evaluate (unsigned var, tree chrec, tree n, unsigned int k)
539 tree arg0, arg1, binomial_n_k;
540 tree type = TREE_TYPE (chrec);
541 struct loop *var_loop = get_loop (var);
543 while (TREE_CODE (chrec) == POLYNOMIAL_CHREC
544 && flow_loop_nested_p (var_loop, get_chrec_loop (chrec)))
545 chrec = CHREC_LEFT (chrec);
547 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC
548 && CHREC_VARIABLE (chrec) == var)
550 arg1 = chrec_evaluate (var, CHREC_RIGHT (chrec), n, k + 1);
551 if (arg1 == chrec_dont_know)
552 return chrec_dont_know;
553 binomial_n_k = tree_fold_binomial (type, n, k);
555 return chrec_dont_know;
556 arg0 = fold_build2 (MULT_EXPR, type,
557 CHREC_LEFT (chrec), binomial_n_k);
558 return chrec_fold_plus (type, arg0, arg1);
561 binomial_n_k = tree_fold_binomial (type, n, k);
563 return chrec_dont_know;
565 return fold_build2 (MULT_EXPR, type, chrec, binomial_n_k);
568 /* Evaluates "CHREC (X)" when the varying variable is VAR.
569 Example: Given the following parameters,
575 The result is given by the Newton's interpolating formula:
576 3 * \binom{10}{0} + 4 * \binom{10}{1}.
580 chrec_apply (unsigned var,
584 tree type = chrec_type (chrec);
585 tree res = chrec_dont_know;
587 if (automatically_generated_chrec_p (chrec)
588 || automatically_generated_chrec_p (x)
590 /* When the symbols are defined in an outer loop, it is possible
591 to symbolically compute the apply, since the symbols are
592 constants with respect to the varying loop. */
593 || chrec_contains_symbols_defined_in_loop (chrec, var))
594 return chrec_dont_know;
596 if (dump_file && (dump_flags & TDF_DETAILS))
597 fprintf (dump_file, "(chrec_apply \n");
599 if (TREE_CODE (x) == INTEGER_CST && SCALAR_FLOAT_TYPE_P (type))
600 x = build_real_from_int_cst (type, x);
602 if (evolution_function_is_affine_p (chrec))
604 /* "{a, +, b} (x)" -> "a + b*x". */
605 x = chrec_convert_rhs (type, x, NULL);
606 res = chrec_fold_multiply (TREE_TYPE (x), CHREC_RIGHT (chrec), x);
607 res = chrec_fold_plus (type, CHREC_LEFT (chrec), res);
610 else if (TREE_CODE (chrec) != POLYNOMIAL_CHREC)
613 else if (TREE_CODE (x) == INTEGER_CST
614 && tree_int_cst_sgn (x) == 1)
615 /* testsuite/.../ssa-chrec-38.c. */
616 res = chrec_evaluate (var, chrec, x, 0);
618 res = chrec_dont_know;
620 if (dump_file && (dump_flags & TDF_DETAILS))
622 fprintf (dump_file, " (varying_loop = %d\n", var);
623 fprintf (dump_file, ")\n (chrec = ");
624 print_generic_expr (dump_file, chrec, 0);
625 fprintf (dump_file, ")\n (x = ");
626 print_generic_expr (dump_file, x, 0);
627 fprintf (dump_file, ")\n (res = ");
628 print_generic_expr (dump_file, res, 0);
629 fprintf (dump_file, "))\n");
635 /* Replaces the initial condition in CHREC with INIT_COND. */
638 chrec_replace_initial_condition (tree chrec,
641 if (automatically_generated_chrec_p (chrec))
644 gcc_assert (chrec_type (chrec) == chrec_type (init_cond));
646 switch (TREE_CODE (chrec))
648 case POLYNOMIAL_CHREC:
649 return build_polynomial_chrec
650 (CHREC_VARIABLE (chrec),
651 chrec_replace_initial_condition (CHREC_LEFT (chrec), init_cond),
652 CHREC_RIGHT (chrec));
659 /* Returns the initial condition of a given CHREC. */
662 initial_condition (tree chrec)
664 if (automatically_generated_chrec_p (chrec))
667 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
668 return initial_condition (CHREC_LEFT (chrec));
673 /* Returns a univariate function that represents the evolution in
674 LOOP_NUM. Mask the evolution of any other loop. */
677 hide_evolution_in_other_loops_than_loop (tree chrec,
680 struct loop *loop = get_loop (loop_num), *chloop;
681 if (automatically_generated_chrec_p (chrec))
684 switch (TREE_CODE (chrec))
686 case POLYNOMIAL_CHREC:
687 chloop = get_chrec_loop (chrec);
690 return build_polynomial_chrec
692 hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec),
694 CHREC_RIGHT (chrec));
696 else if (flow_loop_nested_p (chloop, loop))
697 /* There is no evolution in this loop. */
698 return initial_condition (chrec);
702 gcc_assert (flow_loop_nested_p (loop, chloop));
703 return hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec),
712 /* Returns the evolution part of CHREC in LOOP_NUM when RIGHT is
713 true, otherwise returns the initial condition in LOOP_NUM. */
716 chrec_component_in_loop_num (tree chrec,
721 struct loop *loop = get_loop (loop_num), *chloop;
723 if (automatically_generated_chrec_p (chrec))
726 switch (TREE_CODE (chrec))
728 case POLYNOMIAL_CHREC:
729 chloop = get_chrec_loop (chrec);
734 component = CHREC_RIGHT (chrec);
736 component = CHREC_LEFT (chrec);
738 if (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC
739 || CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec))
743 return build_polynomial_chrec
745 chrec_component_in_loop_num (CHREC_LEFT (chrec),
751 else if (flow_loop_nested_p (chloop, loop))
752 /* There is no evolution part in this loop. */
757 gcc_assert (flow_loop_nested_p (loop, chloop));
758 return chrec_component_in_loop_num (CHREC_LEFT (chrec),
771 /* Returns the evolution part in LOOP_NUM. Example: the call
772 evolution_part_in_loop_num ({{0, +, 1}_1, +, 2}_1, 1) returns
776 evolution_part_in_loop_num (tree chrec,
779 return chrec_component_in_loop_num (chrec, loop_num, true);
782 /* Returns the initial condition in LOOP_NUM. Example: the call
783 initial_condition_in_loop_num ({{0, +, 1}_1, +, 2}_2, 2) returns
787 initial_condition_in_loop_num (tree chrec,
790 return chrec_component_in_loop_num (chrec, loop_num, false);
793 /* Set or reset the evolution of CHREC to NEW_EVOL in loop LOOP_NUM.
794 This function is essentially used for setting the evolution to
795 chrec_dont_know, for example after having determined that it is
796 impossible to say how many times a loop will execute. */
799 reset_evolution_in_loop (unsigned loop_num,
803 struct loop *loop = get_loop (loop_num);
805 if (POINTER_TYPE_P (chrec_type (chrec)))
806 gcc_assert (sizetype == chrec_type (new_evol));
808 gcc_assert (chrec_type (chrec) == chrec_type (new_evol));
810 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC
811 && flow_loop_nested_p (loop, get_chrec_loop (chrec)))
813 tree left = reset_evolution_in_loop (loop_num, CHREC_LEFT (chrec),
815 tree right = reset_evolution_in_loop (loop_num, CHREC_RIGHT (chrec),
817 return build3 (POLYNOMIAL_CHREC, TREE_TYPE (left),
818 build_int_cst (NULL_TREE, CHREC_VARIABLE (chrec)),
822 while (TREE_CODE (chrec) == POLYNOMIAL_CHREC
823 && CHREC_VARIABLE (chrec) == loop_num)
824 chrec = CHREC_LEFT (chrec);
826 return build_polynomial_chrec (loop_num, chrec, new_evol);
829 /* Merges two evolution functions that were found by following two
830 alternate paths of a conditional expression. */
833 chrec_merge (tree chrec1,
836 if (chrec1 == chrec_dont_know
837 || chrec2 == chrec_dont_know)
838 return chrec_dont_know;
840 if (chrec1 == chrec_known
841 || chrec2 == chrec_known)
844 if (chrec1 == chrec_not_analyzed_yet)
846 if (chrec2 == chrec_not_analyzed_yet)
849 if (eq_evolutions_p (chrec1, chrec2))
852 return chrec_dont_know;
859 /* Helper function for is_multivariate_chrec. */
862 is_multivariate_chrec_rec (const_tree chrec, unsigned int rec_var)
864 if (chrec == NULL_TREE)
867 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
869 if (CHREC_VARIABLE (chrec) != rec_var)
872 return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), rec_var)
873 || is_multivariate_chrec_rec (CHREC_RIGHT (chrec), rec_var));
879 /* Determine whether the given chrec is multivariate or not. */
882 is_multivariate_chrec (const_tree chrec)
884 if (chrec == NULL_TREE)
887 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
888 return (is_multivariate_chrec_rec (CHREC_LEFT (chrec),
889 CHREC_VARIABLE (chrec))
890 || is_multivariate_chrec_rec (CHREC_RIGHT (chrec),
891 CHREC_VARIABLE (chrec)));
896 /* Determines whether the chrec contains symbolic names or not. */
899 chrec_contains_symbols (const_tree chrec)
903 if (chrec == NULL_TREE)
906 if (TREE_CODE (chrec) == SSA_NAME
907 || TREE_CODE (chrec) == VAR_DECL
908 || TREE_CODE (chrec) == PARM_DECL
909 || TREE_CODE (chrec) == FUNCTION_DECL
910 || TREE_CODE (chrec) == LABEL_DECL
911 || TREE_CODE (chrec) == RESULT_DECL
912 || TREE_CODE (chrec) == FIELD_DECL)
915 n = TREE_OPERAND_LENGTH (chrec);
916 for (i = 0; i < n; i++)
917 if (chrec_contains_symbols (TREE_OPERAND (chrec, i)))
922 /* Determines whether the chrec contains undetermined coefficients. */
925 chrec_contains_undetermined (const_tree chrec)
929 if (chrec == chrec_dont_know)
932 if (chrec == NULL_TREE)
935 n = TREE_OPERAND_LENGTH (chrec);
936 for (i = 0; i < n; i++)
937 if (chrec_contains_undetermined (TREE_OPERAND (chrec, i)))
942 /* Determines whether the tree EXPR contains chrecs, and increment
943 SIZE if it is not a NULL pointer by an estimation of the depth of
947 tree_contains_chrecs (const_tree expr, int *size)
951 if (expr == NULL_TREE)
957 if (tree_is_chrec (expr))
960 n = TREE_OPERAND_LENGTH (expr);
961 for (i = 0; i < n; i++)
962 if (tree_contains_chrecs (TREE_OPERAND (expr, i), size))
967 /* Recursive helper function. */
970 evolution_function_is_invariant_rec_p (tree chrec, int loopnum)
972 if (evolution_function_is_constant_p (chrec))
975 if (TREE_CODE (chrec) == SSA_NAME
977 || expr_invariant_in_loop_p (get_loop (loopnum), chrec)))
980 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
982 if (CHREC_VARIABLE (chrec) == (unsigned) loopnum
983 || !evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec),
985 || !evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec),
991 switch (TREE_OPERAND_LENGTH (chrec))
994 if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 1),
999 if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 0),
1011 /* Return true if CHREC is invariant in loop LOOPNUM, false otherwise. */
1014 evolution_function_is_invariant_p (tree chrec, int loopnum)
1016 return evolution_function_is_invariant_rec_p (chrec, loopnum);
1019 /* Determine whether the given tree is an affine multivariate
1023 evolution_function_is_affine_multivariate_p (const_tree chrec, int loopnum)
1025 if (chrec == NULL_TREE)
1028 switch (TREE_CODE (chrec))
1030 case POLYNOMIAL_CHREC:
1031 if (evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec), loopnum))
1033 if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), loopnum))
1037 if (TREE_CODE (CHREC_RIGHT (chrec)) == POLYNOMIAL_CHREC
1038 && CHREC_VARIABLE (CHREC_RIGHT (chrec))
1039 != CHREC_VARIABLE (chrec)
1040 && evolution_function_is_affine_multivariate_p
1041 (CHREC_RIGHT (chrec), loopnum))
1049 if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), loopnum)
1050 && TREE_CODE (CHREC_LEFT (chrec)) == POLYNOMIAL_CHREC
1051 && CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec)
1052 && evolution_function_is_affine_multivariate_p
1053 (CHREC_LEFT (chrec), loopnum))
1064 /* Determine whether the given tree is a function in zero or one
1068 evolution_function_is_univariate_p (const_tree chrec)
1070 if (chrec == NULL_TREE)
1073 switch (TREE_CODE (chrec))
1075 case POLYNOMIAL_CHREC:
1076 switch (TREE_CODE (CHREC_LEFT (chrec)))
1078 case POLYNOMIAL_CHREC:
1079 if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_LEFT (chrec)))
1081 if (!evolution_function_is_univariate_p (CHREC_LEFT (chrec)))
1089 switch (TREE_CODE (CHREC_RIGHT (chrec)))
1091 case POLYNOMIAL_CHREC:
1092 if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_RIGHT (chrec)))
1094 if (!evolution_function_is_univariate_p (CHREC_RIGHT (chrec)))
1107 /* Returns the number of variables of CHREC. Example: the call
1108 nb_vars_in_chrec ({{0, +, 1}_5, +, 2}_6) returns 2. */
1111 nb_vars_in_chrec (tree chrec)
1113 if (chrec == NULL_TREE)
1116 switch (TREE_CODE (chrec))
1118 case POLYNOMIAL_CHREC:
1119 return 1 + nb_vars_in_chrec
1120 (initial_condition_in_loop_num (chrec, CHREC_VARIABLE (chrec)));
1127 static tree chrec_convert_1 (tree, tree, gimple, bool);
1129 /* Converts BASE and STEP of affine scev to TYPE. LOOP is the loop whose iv
1130 the scev corresponds to. AT_STMT is the statement at that the scev is
1131 evaluated. USE_OVERFLOW_SEMANTICS is true if this function should assume that
1132 the rules for overflow of the given language apply (e.g., that signed
1133 arithmetics in C does not overflow) -- i.e., to use them to avoid unnecessary
1134 tests, but also to enforce that the result follows them. Returns true if the
1135 conversion succeeded, false otherwise. */
1138 convert_affine_scev (struct loop *loop, tree type,
1139 tree *base, tree *step, gimple at_stmt,
1140 bool use_overflow_semantics)
1142 tree ct = TREE_TYPE (*step);
1143 bool enforce_overflow_semantics;
1144 bool must_check_src_overflow, must_check_rslt_overflow;
1145 tree new_base, new_step;
1146 tree step_type = POINTER_TYPE_P (type) ? sizetype : type;
1149 (TYPE) (BASE + STEP * i) = (TYPE) BASE + (TYPE -- sign extend) STEP * i,
1150 but we must check some assumptions.
1152 1) If [BASE, +, STEP] wraps, the equation is not valid when precision
1153 of CT is smaller than the precision of TYPE. For example, when we
1154 cast unsigned char [254, +, 1] to unsigned, the values on left side
1155 are 254, 255, 0, 1, ..., but those on the right side are
1156 254, 255, 256, 257, ...
1157 2) In case that we must also preserve the fact that signed ivs do not
1158 overflow, we must additionally check that the new iv does not wrap.
1159 For example, unsigned char [125, +, 1] casted to signed char could
1160 become a wrapping variable with values 125, 126, 127, -128, -127, ...,
1161 which would confuse optimizers that assume that this does not
1163 must_check_src_overflow = TYPE_PRECISION (ct) < TYPE_PRECISION (type);
1165 enforce_overflow_semantics = (use_overflow_semantics
1166 && nowrap_type_p (type));
1167 if (enforce_overflow_semantics)
1169 /* We can avoid checking whether the result overflows in the following
1172 -- must_check_src_overflow is true, and the range of TYPE is superset
1173 of the range of CT -- i.e., in all cases except if CT signed and
1175 -- both CT and TYPE have the same precision and signedness, and we
1176 verify instead that the source does not overflow (this may be
1177 easier than verifying it for the result, as we may use the
1178 information about the semantics of overflow in CT). */
1179 if (must_check_src_overflow)
1181 if (TYPE_UNSIGNED (type) && !TYPE_UNSIGNED (ct))
1182 must_check_rslt_overflow = true;
1184 must_check_rslt_overflow = false;
1186 else if (TYPE_UNSIGNED (ct) == TYPE_UNSIGNED (type)
1187 && TYPE_PRECISION (ct) == TYPE_PRECISION (type))
1189 must_check_rslt_overflow = false;
1190 must_check_src_overflow = true;
1193 must_check_rslt_overflow = true;
1196 must_check_rslt_overflow = false;
1198 if (must_check_src_overflow
1199 && scev_probably_wraps_p (*base, *step, at_stmt, loop,
1200 use_overflow_semantics))
1203 new_base = chrec_convert_1 (type, *base, at_stmt,
1204 use_overflow_semantics);
1205 /* The step must be sign extended, regardless of the signedness
1206 of CT and TYPE. This only needs to be handled specially when
1207 CT is unsigned -- to avoid e.g. unsigned char [100, +, 255]
1208 (with values 100, 99, 98, ...) from becoming signed or unsigned
1209 [100, +, 255] with values 100, 355, ...; the sign-extension is
1210 performed by default when CT is signed. */
1212 if (TYPE_PRECISION (step_type) > TYPE_PRECISION (ct) && TYPE_UNSIGNED (ct))
1213 new_step = chrec_convert_1 (signed_type_for (ct), new_step, at_stmt,
1214 use_overflow_semantics);
1215 new_step = chrec_convert_1 (step_type, new_step, at_stmt, use_overflow_semantics);
1217 if (automatically_generated_chrec_p (new_base)
1218 || automatically_generated_chrec_p (new_step))
1221 if (must_check_rslt_overflow
1222 /* Note that in this case we cannot use the fact that signed variables
1223 do not overflow, as this is what we are verifying for the new iv. */
1224 && scev_probably_wraps_p (new_base, new_step, at_stmt, loop, false))
1233 /* Convert CHREC for the right hand side of a CREC.
1234 The increment for a pointer type is always sizetype. */
1236 chrec_convert_rhs (tree type, tree chrec, gimple at_stmt)
1238 if (POINTER_TYPE_P (type))
1240 return chrec_convert (type, chrec, at_stmt);
1243 /* Convert CHREC to TYPE. When the analyzer knows the context in
1244 which the CHREC is built, it sets AT_STMT to the statement that
1245 contains the definition of the analyzed variable, otherwise the
1246 conversion is less accurate: the information is used for
1247 determining a more accurate estimation of the number of iterations.
1248 By default AT_STMT could be safely set to NULL_TREE.
1250 The following rule is always true: TREE_TYPE (chrec) ==
1251 TREE_TYPE (CHREC_LEFT (chrec)) == TREE_TYPE (CHREC_RIGHT (chrec)).
1252 An example of what could happen when adding two chrecs and the type
1253 of the CHREC_RIGHT is different than CHREC_LEFT is:
1255 {(uint) 0, +, (uchar) 10} +
1256 {(uint) 0, +, (uchar) 250}
1258 that would produce a wrong result if CHREC_RIGHT is not (uint):
1260 {(uint) 0, +, (uchar) 4}
1264 {(uint) 0, +, (uint) 260}
1268 chrec_convert (tree type, tree chrec, gimple at_stmt)
1270 return chrec_convert_1 (type, chrec, at_stmt, true);
1273 /* Convert CHREC to TYPE. When the analyzer knows the context in
1274 which the CHREC is built, it sets AT_STMT to the statement that
1275 contains the definition of the analyzed variable, otherwise the
1276 conversion is less accurate: the information is used for
1277 determining a more accurate estimation of the number of iterations.
1278 By default AT_STMT could be safely set to NULL_TREE.
1280 USE_OVERFLOW_SEMANTICS is true if this function should assume that
1281 the rules for overflow of the given language apply (e.g., that signed
1282 arithmetics in C does not overflow) -- i.e., to use them to avoid unnecessary
1283 tests, but also to enforce that the result follows them. */
1286 chrec_convert_1 (tree type, tree chrec, gimple at_stmt,
1287 bool use_overflow_semantics)
1293 if (automatically_generated_chrec_p (chrec))
1296 ct = chrec_type (chrec);
1300 if (!evolution_function_is_affine_p (chrec))
1303 loop = get_chrec_loop (chrec);
1304 base = CHREC_LEFT (chrec);
1305 step = CHREC_RIGHT (chrec);
1307 if (convert_affine_scev (loop, type, &base, &step, at_stmt,
1308 use_overflow_semantics))
1309 return build_polynomial_chrec (loop->num, base, step);
1311 /* If we cannot propagate the cast inside the chrec, just keep the cast. */
1313 /* Fold will not canonicalize (long)(i - 1) to (long)i - 1 because that
1314 may be more expensive. We do want to perform this optimization here
1315 though for canonicalization reasons. */
1316 if (use_overflow_semantics
1317 && (TREE_CODE (chrec) == PLUS_EXPR
1318 || TREE_CODE (chrec) == MINUS_EXPR)
1319 && TREE_CODE (type) == INTEGER_TYPE
1320 && TREE_CODE (ct) == INTEGER_TYPE
1321 && TYPE_PRECISION (type) > TYPE_PRECISION (ct)
1322 && TYPE_OVERFLOW_UNDEFINED (ct))
1323 res = fold_build2 (TREE_CODE (chrec), type,
1324 fold_convert (type, TREE_OPERAND (chrec, 0)),
1325 fold_convert (type, TREE_OPERAND (chrec, 1)));
1327 res = fold_convert (type, chrec);
1329 /* Don't propagate overflows. */
1330 if (CONSTANT_CLASS_P (res))
1331 TREE_OVERFLOW (res) = 0;
1333 /* But reject constants that don't fit in their type after conversion.
1334 This can happen if TYPE_MIN_VALUE or TYPE_MAX_VALUE are not the
1335 natural values associated with TYPE_PRECISION and TYPE_UNSIGNED,
1336 and can cause problems later when computing niters of loops. Note
1337 that we don't do the check before converting because we don't want
1338 to reject conversions of negative chrecs to unsigned types. */
1339 if (TREE_CODE (res) == INTEGER_CST
1340 && TREE_CODE (type) == INTEGER_TYPE
1341 && !int_fits_type_p (res, type))
1342 res = chrec_dont_know;
1347 /* Convert CHREC to TYPE, without regard to signed overflows. Returns the new
1348 chrec if something else than what chrec_convert would do happens, NULL_TREE
1352 chrec_convert_aggressive (tree type, tree chrec)
1354 tree inner_type, left, right, lc, rc, rtype;
1356 if (automatically_generated_chrec_p (chrec)
1357 || TREE_CODE (chrec) != POLYNOMIAL_CHREC)
1360 inner_type = TREE_TYPE (chrec);
1361 if (TYPE_PRECISION (type) > TYPE_PRECISION (inner_type))
1364 rtype = POINTER_TYPE_P (type) ? sizetype : type;
1366 left = CHREC_LEFT (chrec);
1367 right = CHREC_RIGHT (chrec);
1368 lc = chrec_convert_aggressive (type, left);
1370 lc = chrec_convert (type, left, NULL);
1371 rc = chrec_convert_aggressive (rtype, right);
1373 rc = chrec_convert (rtype, right, NULL);
1375 return build_polynomial_chrec (CHREC_VARIABLE (chrec), lc, rc);
1378 /* Returns true when CHREC0 == CHREC1. */
1381 eq_evolutions_p (const_tree chrec0, const_tree chrec1)
1383 if (chrec0 == NULL_TREE
1384 || chrec1 == NULL_TREE
1385 || TREE_CODE (chrec0) != TREE_CODE (chrec1))
1388 if (chrec0 == chrec1)
1391 switch (TREE_CODE (chrec0))
1394 return operand_equal_p (chrec0, chrec1, 0);
1396 case POLYNOMIAL_CHREC:
1397 return (CHREC_VARIABLE (chrec0) == CHREC_VARIABLE (chrec1)
1398 && eq_evolutions_p (CHREC_LEFT (chrec0), CHREC_LEFT (chrec1))
1399 && eq_evolutions_p (CHREC_RIGHT (chrec0), CHREC_RIGHT (chrec1)));
1405 /* Returns EV_GROWS if CHREC grows (assuming that it does not overflow),
1406 EV_DECREASES if it decreases, and EV_UNKNOWN if we cannot determine
1407 which of these cases happens. */
1410 scev_direction (const_tree chrec)
1414 if (!evolution_function_is_affine_p (chrec))
1415 return EV_DIR_UNKNOWN;
1417 step = CHREC_RIGHT (chrec);
1418 if (TREE_CODE (step) != INTEGER_CST)
1419 return EV_DIR_UNKNOWN;
1421 if (tree_int_cst_sign_bit (step))
1422 return EV_DIR_DECREASES;
1424 return EV_DIR_GROWS;
1427 /* Iterates over all the components of SCEV, and calls CBCK. */
1430 for_each_scev_op (tree *scev, bool (*cbck) (tree *, void *), void *data)
1432 switch (TREE_CODE_LENGTH (TREE_CODE (*scev)))
1435 for_each_scev_op (&TREE_OPERAND (*scev, 2), cbck, data);
1438 for_each_scev_op (&TREE_OPERAND (*scev, 1), cbck, data);
1441 for_each_scev_op (&TREE_OPERAND (*scev, 0), cbck, data);
1449 /* Returns true when the operation can be part of a linear
1453 operator_is_linear (tree scev)
1455 switch (TREE_CODE (scev))
1458 case POLYNOMIAL_CHREC:
1460 case POINTER_PLUS_EXPR:
1465 case NON_LVALUE_EXPR:
1475 /* Return true when SCEV is a linear expression. Linear expressions
1476 can contain additions, substractions and multiplications.
1477 Multiplications are restricted to constant scaling: "cst * x". */
1480 scev_is_linear_expression (tree scev)
1483 || !operator_is_linear (scev))
1486 if (TREE_CODE (scev) == MULT_EXPR)
1487 return !(tree_contains_chrecs (TREE_OPERAND (scev, 0), NULL)
1488 && tree_contains_chrecs (TREE_OPERAND (scev, 1), NULL));
1490 if (TREE_CODE (scev) == POLYNOMIAL_CHREC
1491 && !evolution_function_is_affine_multivariate_p (scev, CHREC_VARIABLE (scev)))
1494 switch (TREE_CODE_LENGTH (TREE_CODE (scev)))
1497 return scev_is_linear_expression (TREE_OPERAND (scev, 0))
1498 && scev_is_linear_expression (TREE_OPERAND (scev, 1))
1499 && scev_is_linear_expression (TREE_OPERAND (scev, 2));
1502 return scev_is_linear_expression (TREE_OPERAND (scev, 0))
1503 && scev_is_linear_expression (TREE_OPERAND (scev, 1));
1506 return scev_is_linear_expression (TREE_OPERAND (scev, 0));
1516 /* Determines whether the expression CHREC contains only interger consts
1517 in the right parts. */
1520 evolution_function_right_is_integer_cst (const_tree chrec)
1522 if (chrec == NULL_TREE)
1525 switch (TREE_CODE (chrec))
1530 case POLYNOMIAL_CHREC:
1531 return TREE_CODE (CHREC_RIGHT (chrec)) == INTEGER_CST
1532 && (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC
1533 || evolution_function_right_is_integer_cst (CHREC_LEFT (chrec)));
1536 return evolution_function_right_is_integer_cst (TREE_OPERAND (chrec, 0));